Cueing end-effector acceleration of a two-link robotic arm by dynamic averaged sub-gradient integral sliding mode control

The primary objective of this research is to determine if the dynamic version of an averaged sub-gradient (ASG) integral siding mode (ISM) controller can effectively handle the end-effector acceleration tracking problem for a two-link robotic arm avoiding singularity conditions. The proposed scheme solves a nonlinear extremum seeking problem that minimizes a non-strictly convex function that depends on the acceleration tracking error defined by the difference between the desired acceleration trajectory and the cueing end-effector acceleration of a two-link robotic arm in a 2D-plane. A second-order differential equation drives the proposed dynamic ASG with nonlinear coefficients and a discontinuous right-hand side term, which allows for the achievement of the necessary ISM regime in the presence of considerable errors in the mathematical model description. A special switch between modes allows the controller to track accelerations even in extreme positions (near to the active boundaries of the joint articulations) effectively.